Everyone has a minhag.
The Maharil brings down that you are “mechuyav” to sit in the sukka on Shmini Atzeres “afilu l’hashmi’a shmu’os” which really refers to learning or “talking in Torah.”
Minhagim vary but that is the basis. So “Shtiky,” check what your father/gfather’s minhag.
There is no problem in sitting in the sukka all year round–just no brocho.
So there is no issur of sitting in the sukka on Shmini Atzeres. Insofar as Arba Minnim, there is a problem of a “tarta d’sasra” so even though it is be a “yom tov sheni” of Hoshana Rabbo, we end up with a mitzvos d’rabbonon (lulav, hoshanas) which cannot override the d’oraisa of Shmini Atzeres, so we end with a Shev v’al Ta’asse for those d’rabbonon’s from Succos.
Have a wonderful yom tov.